Kim and Jane invested the same amount in two different types of investment plans.
After a certain period, Kim earned 10 times of what he invested and Jane earned $31.5 more than 5.5 times of the money she invested.
If Kim's earning is more than Jane's earning, find the minimum amount they invested at the beginning.
Let x be the money they invested at the beginning.
So, after a certain period,
Kim's earnings = 10x and
Jane's earnings = 5.5x + 31.5
Since Kim earned more than Jane,
10x > 5.5x + 31.5.